BOSTON — Courting unions on Labor Day, President Barack Obama denounced Republicans for a “constant attack on working Americans” and said he was using his executive power to force federal contractors to give paid sick leave to their employees.

Obama was met with resounding applause at a major union rally and breakfast in Boston on Monday when he said he had signed the executive order aboard Air Force One as he flew in to mark Labor Day. He said Republicans who claim the mantle of middle-class protectors are talking big, but they “have to walk the walk.”

Obama said opponents of his economic policies “won’t let facts or evidence get in their way.”

The Labor Day gesture to workers’ groups came as Obama works to smooth over tensions with the labor movement over his trade agenda. Major unions are opposing Obama’s push for sweeping new trade deals with Asia and Europe, with some threatening to work against Democrats who voted to support those talks in Congress. Unions have warned that the deals could lead to the widespread job elimination. Obama has signed a law providing money to retrain workers if their jobs get shipped overseas.

The White House wouldn’t specify the cost to federal contractors to implement the executive order. The Labor Department said any costs would be offset by savings that contractors would see as a result of lower attrition rates and increased worker loyalty.